Which statements are true of the function f(x) = 3(2.5)x? check all that apply. the function is exponential. the initial value of the function is 2.5. the function increases by a factor of 2.5 for each unit increase in x. the domain of the function is all real numbers. the range of the function is all real numbers greater than 3.

The statements which are true of the function; f(x) = 3(2.5)^x and there explanations are below;

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This is an exponential function since the x is in the exponent's place instead of in the place of a "regular" variable. The first statement is true.

The initial value of this particular function is 3 (the other number is the multiplier), so choice 2 is NOT true.

The function increases by its multiplier, which is 2.5, so statement 3 is true.

The equation allows us to enter any x value we want to determine the y, so the domain is in fact all real numbers. So, this statement is also true.

If you were to graph this on a calculator, you would see that the range, the "allowed" y values for our function, do not touch or ever drop below the x-axis. That means that the range is all numbers greater than 0. So that statement is false. No matter what value we pick for x, we will NEVER get back a negative y value or that y = 0. For example, if x = 0, y = 3; if x = -5, y = .03; if x = -10, y = .0003; if x = 5, y = 292.97; if x = -100, . Y will never be equal to 0 or less than 0.

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